Question

Barton took out a car loan of $2,625. He makes monthly payments of $175. The graph represents the remaining balance after each payment. Which example models the correct slope?

(1 point)
Responses

m=1,050−1,2259−8
m equals Start Fraction 1,050 minus 1,225 over 9 minus 8 End Fraction

m=2,450−2,6250−1
m equals Start Fraction 2,450 minus 2,625 over 0 minus 1 End Fraction

m=525−70011−12
m equals Start Fraction 525 minus 700 over 11 minus 12 End Fraction

m=9−81,050−1,225

Answer 1

To find the correct slope that models the situation of Barton taking out a car loan of $2,625 and making monthly payments of $175, we need to determine how the remaining balance changes with each payment.

Given:
- Initial balance (loan amount): $2,625
- Monthly payment: $175

After \( n \) months, the remaining balance can be modeled as:
\[ \text{Remaining balance} = 2,625 - 175n \]

We can represent the changes in the remaining balance using two points on the graph based on the remaining balance after payments:
1. After 0 months, remaining balance = $2,625.
2. After 1 month, remaining balance = $2,625 - $175 = $2,450.

Now, we can calculate the slope (m) using these two points:
- Point 1: (0, 2,625)
- Point 2: (1, 2,450)

The formula for the slope \( m \) between these two points is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2,450 - 2,625}{1 - 0} = \frac{-175}{1} = -175 \]

Now, we look at the options provided:

1. \( m = \frac{1,050 - 1,225}{9 - 8} \)
2. \( m = \frac{2,450 - 2,625}{0 - 1} \)
3. \( m = \frac{525 - 700}{11 - 12} \)
4. \( m = \frac{9 - 8}{1,050 - 1,225} \)

To see which one matches our calculation of -175, we can evaluate each option:

1. \( m = \frac{1,050 - 1,225}{9 - 8} = \frac{-175}{1} = -175 \)
2. \( m = \frac{2,450 - 2,625}{0 - 1} = \frac{-175}{-1} = 175 \)
3. \( m = \frac{525 - 700}{11 - 12} = \frac{-175}{-1} = 175 \)
4. \( m = \frac{9 - 8}{1,050 - 1,225} \) is not computable as it refers to different values.

Based on our calculations, the correct slope that models the situation is:
**Option 1: \( m = \frac{1,050 - 1,225}{9 - 8} \)**.